Stochastic modelling for systems biology
Stage 3 project, 2026/27
- Supervisor: Darren Wilkinson
- Project research area: Statistics
Project outline
At high concentrations, chemical reactions and related processes can be viewed as continuous and deterministic, and be well-described by ODEs and PDEs. However, down at the level of single cells, many biochemical processes take place at such low concentrations that the discreteness of the molecules involved cannot be ignored, and stochastic processes must be used to obtain satisfactory descriptions of the discrete random reaction dynamics. This project will be concerned with computational modelling and stochastic simulation of such continuous-time Markov processes, and the fitting of such models to time course experimental data.
Group project
The group project will be concerned with developing the foundational understanding of stochastic approaches to systems biology modelling.
By the end of the group project you will have learned:
- Mathematical modelling of biological processes as chemical reaction networks
- Markov processes in continuous time
- Stochastic simulation of Markov processes
- Modelling chemical reaction networks as Markov (jump) processes
- Gillespie’s algorithm for discrete stochastic simulation of chemical reaction networks
- Examples of classic genetic and biochemical reaction networks
By the end of the group project you will be able to:
- Understand the mathematical foundations of stochastic systems biology modelling
- Mathematically represent biological processes as chemical reaction networks
- Represent chemical reaction networks in computer code
- Use the Python programming language for modelling and stochastic simulation
- Stochastically simulate reaction networks on a computer in order to better understand their properties
Mode of operation and evidence of learning
The project will involve learning through reading and discussion, and programming in Python. Students will demonstrate their understanding by building models of biological processes, comparing theory to simulation results, writing code to implement core methodology, and carrying out simulation experiments. Students will clearly communicate the material in both written and oral formats.
Individual project
Potential areas for more in-depth study include:
- Fast exact and approximate simulation algorithms
- Compositional modelling of large reaction networks
- Bayesian inference for stochastic kinetic models
- Simulation of stochastic reaction-diffusion processes
- Detailed modelling and analysis for a real non-trivial genetic/biochemical network
Mode of operation and evidence of learning
The project will involve learning through reading and discussion, and programming in Python. Students will demonstrate their understanding by building models of biological processes, comparing theory to simulation results, writing code to implement core methodology, and carrying out simulation experiments. Students will clearly communicate the material in both written and oral formats.
Pre-requisites
You should have a strong background in probability and statistics, and must be comfortable with programming in Python (despite being a statistics project, Python is recommended in preference to R). MATH3421 (BCM III) is highly recommended as a co-requisite. MATH3171 (MB III) would also be advantageous. You should be taking at least one of these modules alongside this group project.
Some relevant resources
Books
- Wilkinson, D. J. (2018) Stochastic modelling for systems biology, third edition, Chapman & Hall/CRC Press.
- Wilkinson, D. J. (2026) Stochastic modelling for systems biology with Python, Chapman & Hall/CRC Press, in preparation (a draft PDF will be available by October).
- Erban, R., Chapman, S. J. (2020) Stochastic modelling of reaction-diffusion processes, Cambridge texts in applied mathematics.
Papers
- Wilkinson, D. J. (2025) jax-smfsb: A Python library for stochastic systems biology modelling and inference, The Journal of Open Source Software, 10(106):7491.
- Wilkinson, D. J. (2009) Stochastic modelling for quantitative description of heterogeneous biological systems, Nature Reviews Genetics, 10(2):122-133.
- Golightly, A., Wilkinson, D. J. (2011) Bayesian parameter inference for stochastic biochemical network models using particle MCMC, Interface Focus, 1(6):807-820.
- Keating, S., et al. (2020) SBML Level 3: an extensible format for the exchange and reuse of biological models, Molecular Systems Biology, 16(8):e9110.
- Salis, H., Kaznessis, Y. N. (2005) Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions, Journal of Chemical Physics, 122(5): 054103.
- Ghosh, A. et al (2015) The spatial chemical Langevin equation and reaction diffusion master equations: moments and qualitative solutions, Theoretical Biology and Medical Modelling, 12:5.
- Smith, S., Grima, R. (2019) Spatial stochastic intracellular kinetics: a review of modelling approaches, Bulletin of Mathematical Biology, 81, 2960-3009.
- Tian, T., Burrage, K. (2006) Stochastic models for regulatory networks of the genetic toggle switch, PNAS, 103(22):8372-8377.
- Arkin, A., Ross, J, McAdams, H. H. (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells, Genetics, 149(4):1633-1648.
- Robb, M. L., Shahrezaei, V. (2014) Stochastic Cellular Fate Decision Making by Multiple Infecting Lambda Phage, PLoS ONE, 9(8): e103636.